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I am building my own power amp. Before I hook up to the real speaker, I want to make sure it is stable and not oscillating. I don't want to just use a 4ohm or 8ohm resistor as speaker is reactive and can cause instability where resistor won't. Anyone have a circuit for a dummy load that has reactance similar to a real multiway speaker?

I am building my own power amp. Before I hook up to the real speaker, I want to make sure it is stable and not oscillating. I don't want to just use a 4ohm or 8ohm resistor as speaker is reactive and can cause instability where resistor won't. Anyone have a circuit for a dummy load that has reactance similar to a real multiway speaker?

From this forum (NOT MINE). It appears that the speaker supplies the inductive component, while the resistor handles the excess load. It would make sense that if you need more than 50 W capacity, you would build in the appropriate parallel resistors.

Anyone have a circuit for a dummy load that has reactance similar to a real multiway speaker?

First the short answer... no.

Now the longer answer. And I'm only going to talk about a single driver (speaker) here. It's impedance function is complicated enough without adding the specifics of a crossover and multiple drivers.

Over the frequency range of a speaker it's response changes from capacitive, to restive, to inductive, and all points in-between. Lets start by examining a typical driver response plot. Below is a response plot typical of a roughly 6Ω driver.

Attachment:

Impedance-phase-free-air.png

This is the response of just the driver without any crossover or cabinet. It also assumes a VERY small driving impedance (nearly zero).

The solid black line is the real part of the impedance plotted across frequency. You can think of this as the effective resistance (although it's really not). The dotted line is the phase angle between the current and voltage waveforms (This is really just the arcTangent of the ratio of real to imaginary impedance).

The first thing that you should notice is that the "impedance" changes radically over frequency. In this case rising to about 10 times the rated impedance of the driver at the natural resonance frequency. So just using a fixed resistor to represent a speaker is not possible. The second thing you should notice is that the phase angle also changes radically across frequency; swinging from positive, to negative, and back to positive again.

Without going into all the math, when the phase angle is positive, the load is said to have an "inductive" character. This is not to say that it behaves as a pure inductor would, just that it has a voltage-current relationship that leans in that direction. When the phase angle is negative, the load is said to have a "capacitative" character. Again, not that it really behaves like a capacitor, only that the voltage-current phase relationship leans in that direction.

So going back to the plot (working left to right). This particular driver starts out mildly inductive, growing more so until in the vicinity of the natural resonance frequency, At resonance, the impedance flips and the driver looks capacitative and then slowly reduces it "capacitative nature" until reaching a purely resistive character at about 1kHz. Above 1kHz the speaker begins to look inductive again, with the "inductive nature" increasing with frequency.

Now here's the kicker, this is all single tone data. But if one feeds two tones into the speaker, say one at 200Hz and one at 2kHz, the lower frequency wave will see a "capacitive nature" load and the higher frequency wave will see an "inductive nature" load... AT THE SAME TIME!

At this point you should be realizing that attempting to simulate this behavior with lumped restive, capacitative, and inductance elements is a fool's errand. Due to the superposition of the different responses across frequency, one can't make it work. Theoretically you could build a circuit that would represent the load at a single frequency, but then it would be good for testing ONLY at that single frequency.

This is why we all test our power amps the same way. First with a restive load of the rated impedance to check for general stability, then with real speakers to make sure it can handle complex nature of the impedance function.

I hope this all makes sense. I really didn't want to disappoint you, but you're never going to find for what you are looking. Speakers are just too complex to simulate in that manner.

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Thanks Matt. I guess it's too complicated to make a load that resemble speakers with crossover. For single speaker I even have a guitar amp power attenuator that presents a complex load for the amp. But it's not going to be the load for speaker with crossover.

But if you first test with only load resistor, you might still get instability with speaker. How about looking at the gain and phase difference between the input and output to predict stability with resistor load? If you look at the power amp as a non inverted opamp, you should be able to compare the input sine wave vs the output sine wave to see what is the phase difference at a few frequencies. Then the most important is at -3dB frequency. If you have a lot of phase margin, then you should be safe.

How about looking at the gain and phase difference between the input and output to predict stability with resistor load?

Actually whereas this is a necessary condition for stability, it is not a sufficient condition for stability. What you really need to do to predict stability is look at the complex loop gain (i.e. Aß) as a function of frequency. If this is plotted in a polar format, then the sufficient condition for stability is to limit the response to those frequencies for which the curve is outside of the unit circle centered at (1, j0).

Let's see if I can explain in a less mathematical and more conceptual manner. Look at the two plots contained below.

Attachment:

Polar Feedback Diagrams.png

These are polar plots of the complex loop gain Aß (magnitude and phase) as a function of frequency for an inverting amplifier chain (i.e. 180º phase shift at midband frequency). The plot on the left is for amplifier with purely resistive load (note that this is only theoretical because there is always some stay capacitance and inductance in real circuits, but its good approximation at audio frequencies) and the one on the right is for an amplifier with complex reactive loads. As you increase frequency beyond the midband you travel clockwise along these contours from the midband point, when you decrease frequency below the midband point you travel counterclockwise along these contours from the midband point. On the right hand diagram is illustrated the unit circle I mentioned above. At frequencies where the curve is inside this circle, the amplifier is conditionally unstable. If the closed response contour encloses the point (1,j0), then the amplifier is absolutely unstable. This is the classical Nyquist Stability Criteria. So let's talk about what this really means.

Instability happens because there is a frequency response in the feedback loop which falls in the unit circle centered at (1,j0). The instability can happen even if the amplifier is not driven at the frequency in question. If the amplifier is regenerative, random thermal noise will drive it into oscillation. So how do we prevent this? We should take our clues from these two stability diagrams.

Starting with the figure on the right, this amplifier is absolutely stable. As we increase from the midband point the curve starts to approach the instability circle (it's still there even if it's not drawn on that diagram). However, the magnitude of the loop gain decreases so that by the time the frequency is high enough to get to that region the loop gain is insignificant and there are no instability issues. Likewise, as the frequency decreases from midband the same phenomenon is exhibited.

Now moving to the figure on the left something different happens. In this case, as frequency increases, the loop gain doesn't shrink fast enough to keep the response out of the instability region. (In fact, it even increases at some higher frequency point. This represents a response peak at the top end of the pass band.) At the frequencies above the point labeled 'P', the amplifier becomes conditional unstable and ringing or oscillation can occur.

So we see that the critical factor for insuring stability seems to be limiting the complex loop gain, Aß, outside of the pass band. Now there are two ways to accomplish this. One is to limit the feedback ß and let the amplifier run open loop. The problem with this approach is that the amplifier response suffers both in magnitude / phase linearity and distortion at either end of the pass band. The other way to accomplish this is to limit the forward gain A of the amplifier outside of the pass band. This is a much better approach as the effects of feedback are not perturbed and the feedback relation A/(1 - Aß) still works at either end of the pass band. But we also have to be careful of how fast we let phase change outside of the pass band. If the gain does not decrease fast enough and the phase changes bring the response into the right half plane, we risk stability issues.

So the proper approach for amplifier stability is to limit the magnitude of the forward gain outside of the pass band, and to not force too many poles into the rolloff function so we control the rate of phase change verses frequency.

This begins to explain why so many designers have difficulties with stability in feedback operation amplifier circuits. Modern operational amplifiers are very high gain, very linear, and very high bandwidth. If the designer does't take care to control the forward gain frequency response, then there is still significant gain at high frequencies to drive the overall response into the instability region. Add to this the problems with the complexities of a speaker load and things get even more difficult to control. In transformer coupled tube output stages, stability is usually much less of a problem because there are natural bandwidth limitations in the output transformer and the input Miller capacitance of the output stage. In this case, it's the double pole phase characteristic of the transformer high end roll off in conjunction with too much high end bandwidth in other places that usually leads to stability issues.

I hope this explanation helps to put general stability criteria into a more understandable form. If you have questions, just let me know.

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I think it's almost impossible to simulate multiway speakers with crossover because the design of the crossover is different for different speakers. Also speakers are different. I follow the suggestion in Bob Cordell. I don't know whether it's good enough. My amp has a closed loop gain of 21 with 20K feedback resistor and 1K shunt resistor. Cordell's book suggested two separate tests:

1) Lower the 20K feedback resistor to 10K so you cut the closed loop gain by half to 11 and see whether it is still stable.

2) Disconnect the 20K on the output side, add a RC to create a pole about 200KHz to drive the 20K feedback resistor. I use a 270ohm and 1500pF to form a pole at 400KHz. This will decrease the phase margin by 45deg at 400KHz( usual BW of amp) to see whether it will oscillate.

I use burst of square wave to keep the overall power dissipation low. Adjust different amplitude to run through the large signal to cover the beta droop at high signal amplitude. I use 4ohm load which is harder on the amp. This is how I do it, I have no idea whether this is good enough. I am yet to drive real speaker.

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